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dlinn [17]
3 years ago
11

Find the lateral area for the pyramid with the equilateral base

Mathematics
1 answer:
likoan [24]3 years ago
5 0
<h3>The lateral area for the pyramid with the equilateral base is 144 square units</h3>

<em><u>Solution:</u></em>

The given pyramid has 3 lateral triangular side

The figure is attached below

Base of triangle = 12 unit

<em><u>Find the perpendicular</u></em>

By Pythagoras theorem

hypotenuse^2 = opposite^2 + adjacent^2

Therefore,

opposite^2 = 10^2 - 6^2\\\\opposite^2 = 100 - 36\\\\opposite^2 = 64\\\\opposite = 8

<em><u>Find the lateral surface area of 1 triangle</u></em>

\text{ Area of 1 lateral triangle } = \frac{1}{2} \times opposite \times base

\text{ Area of 1 lateral triangle } = \frac{1}{2} \times 8 \times 12\\\\\text{ Area of 1 lateral triangle } = 48

<em><u>Thus, lateral surface area of 3 triangle is:</u></em>

3 x 48 = 144

Thus lateral area for the pyramid with the equilateral base is 144 square units

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find three consecutive numbers such that three times the first number is equal to 9 more than the sum of the other two.
Goryan [66]

Answer:

12, 13, 14

Step-by-step explanation:

Three consecutive numbers means three numbers in a row, so if n is the first number, the second number is one more than  n (which is n+1) and the third number is one more than that (which is n+2)

So three times (3 x) the first number (n) is equal to (=) nine more than (9 +) the sum of the other two ( (n+1) + (n+2) )

3 times n can be written as 3n

So 3n = 9 + (n+1) + (n+2)

3n = 9 + n + 1 + n + 2

3n = 9 + 1 + 2 + n + n

3n = 12 + 2n

Subtract 2n from each side

3n - 2n = 12 + 2n - 2n

1n = 12

n = 12

So the first number is 12, the second number is 12 + 1 (13) and the third number is 12 + 2 (14)

The numbers are 12, 13, 14

Hope this helps :)

6 0
3 years ago
In 1980, James planted a tree that was 1 foot tall. In 1996, that same tree was 51 feet tall. James finds that the height of the
Rashid [163]
Divide and see what you get = 51
7 0
2 years ago
Hey can you keep me please I need this ASAP
natka813 [3]

Hey!

---------------------------------------------------------------------------

Question #1:

Least to greatest: 1.6 x 10^-2, 16%, 0.2, 3/5, 6^-1, √6

---------------------------------------------------------------------------

Question #2:

Greatest to least: 5^7, 9^5, 5.9 x 10^4, 15^4, 7.8 x 10^3

---------------------------------------------------------------------------

Hope This Helps :)

7 0
3 years ago
1) 4x + 3y = -13<br>-5x + 2y = -24​
Nataliya [291]
(4x+3y=-13) * 2
(-5x+2y=-24)*3
_____________
8x+6y=-26
-
-15x+6y=-72
___________
23x=46
X=2
6 0
3 years ago
-4(9n + 9) = -12(4n - 6).
WITCHER [35]

Answer:

n = 9

Step-by-step explanation:

Step 1: Write equation

-4(9n + 9) = -12(4n - 6)

Step 2: Solve for <em>n</em>

<u>Distribute:</u> -36n - 36 = -48n + 72

<u>Add 48n to both sides:</u> 12n - 36 = 72

<u>Add 36 to both sides:</u> 12n = 108

<u>Divide both sides by 12:</u> n = 9

Step 3: Check

<em>Plug in n to verify if it's a solution.</em>

-4(9(9) + 9) = -12(4(9) - 6)

-4(81 + 9) = -12(36 - 6)

-4(90) = -12(30)

-360 = -360

7 0
3 years ago
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